Solid Inner Core of the Earth

The seismic phase PKJKP, which traverses the inner core as a shear wave,
and would provide direct evidence for its solidity, has been difficult to detect.
Using stacked broadband records from the Gra"fenberg array in Germany,
we document a high signal to noise phase, whose arrival time and slowness
agree with theoretical predictions for PKJKP. The back-azimuth of this arrival
is also consistent with predictions for PKJKP as is the comparison with a
pseudo-liquid inner core model. Envelope modeling of the PKJKP waveform
implies a slightly larger shear velocity gradient with depth
in the inner core than that in PREM model.

Figures

(A) Ray paths of PKJKP and PKIKP.
The star and square indicate the
source and GRF array locations, respectively.
(B) The theoretical amplitude ratio of PKJKP
over PKIKP as a function of frequency
based on the reference model PREM, after correcting for transmission and
geometrical spreading.
The reference epicentral distance is $138^o$. Given
the dynamic range of present seismometers, it is unlikely that one could observe PKJKP (or pPKJKP) in the frequency range $
\sim 1.0$ Hz {\it (4)}.
(C) Geographical setting of the event (dot) and GRF seismic array (square).
The solid line is the ray path of PKIKP and the dashed
line is the ray path of PKJKP projected on the earth's surface. The triangle
marks the location of the bottoming point of PKJKP in the inner core. The upper-right
inset shows the source time history of the event characterized by a P phase recorded
at a broadband station (YAK, distance = $80.1^o$) of
the Global Seismographic Network, located in a similar azimuth as GRF. The lower-left
inset illustrates the P-wave radiation pattern in the vertical plane of the great
circle. This event is exceptional: (i) the source duration is less than 9 seconds;
(ii) the expected PKJKP is emitted from the top of the
lobe of the P-wave radiation pattern;
(iii) the potential interfering phases identified in
previous studies {\it (4)(5)},
such as PcPPKIKP, pPcPPKIKP, sPcPPKIKP, and PKKPdf,
are at least 17 seconds away from the predicted
PKJKP arrival time (according to PREM).

(A) Observed vespagram for PKIKP+PKiKP and their
depth phases (the energy level is amplified
1.6 times). The center of the energy
maximum is for a slowness of $\sim 1.9 s/deg$,
which is the average of slownesses of PKIKP (1.85 s/deg)
and PKiKP (2.04 s/deg) predicted from PREM {\it (7)}.
The following weaker energy maximum
corresponds to pPKIKP+pPKiKP, and has the same slowness, as predicted from PREM.
(B) Stacked waveforms for PKIKP+PKiKP and their depth phases
for the energy maximum in (A).
(C) Observed vespagram for the potential PKJKP
(energy level is amplified 40 times). The slowness of
the energy maximum is $\sim -1.6 s/deg$,
close to the
PREM prediction of -1.43 s/deg.
The arrival time is also compatible with PREM (1695 sec for the maximum energy,
compared to a prediction of 1690 sec for the high frequency onset of the pulse).
(D) Stacked waveform corresponding
to the energy maximum in (C).
(E) Vespagram in the back-azimuth and travel time domain.
This shows the direction of arrival of the detected energy, which we identify as PKJKP, in
the negative slowness range of Fig. 2C. The estimated
back-azimuth is $\sim 223^o$, which shows that the observed energy
propagates along the major arc from the source
(the expected back-azimuth of PKJKP is $218.^o$).
This indicates that the observed phase is not a near-array scattered
phase, and provides additional evidence for
its identification as PKJKP.

Synthetic modeling. (A) Waveform modeling of PKIKP+PKiKP as well as pPKIKP+pPKiKP
based on USGS PDE moment tensor.
Both observed (dashed line) and synthetic (solid line)
seismograms are normalized after
applying the bandpass filter (0.06-0.1 Hz). Synthetics are
obtained using DSM {\it (13)}. (B) Synthetic differential seismogram
for the PREM model compared to a true liquid inner core, for which the
shear wave velocity is equal to zero. A (PcPPKIKP),
B (pPcPPKIKP+sPcPPKIKP), and C (PKKPdf) are
artificially enhanced by the assumption of
liquid inner core.
(C) Synthetic differential seismogram
based on the pseudo-liquid inner core used in this paper. We now can clearly see both PKJKP and pPKJKP phases.
The amplitude of PKJKP is approximately
2.2 times larger than that of pPKJKP.

Synthetic vespagrams.
(A) Pseudo-liquid inner core model. Time windows are identical to those
in Figure 2C. Energy level is
amplified 40 times, as in Fig. 2C. D, E, and F
are crust, mantle, or outer core phases, and G is PcPPKIKP.
See Fig. S3 for a plot with energy level amplified only 20 times to
bring out the relative strength of these phases.
(B) Solid inner core model, assuming $Q_\beta =300$. Because the strong mantle phase
E in the synthetic model arrives at the same time as PKJKP, the dominant energy of phase E hides the much
weaker PKJKP, which only slightly distorts the pattern of phase E.
Likewise, pPKJKP slightly distorts the pattern of phase F.
Phases E and F are not present in the observed stacks.
Therefore, we cannot directly use the comparison of observed vespagram to
that predicted by the solid inner core model, and instead, we use a differential seismogram modeling approach,
in which the energy from phases E and F is removed.
(C) Synthetic differential vespagram in the slowness-time domain. This vespagram is calculated for the
solid inner core minus the pseudo-liquid inner core models. The time window is the same as
that in Fig. 3C. The estimated slownesses of the energy maxima are both -1.4 s/deg, as are
the predictions based on PREM. This identifies the two phases in the differential seismogram (Fig. 3C)
as PKJKP and pPKJKP.